When to use: Use DMAIC when an existing process underperforms and the root cause is unknown. Use DMADV/DFSS instead when the process does not exist yet or must be redesigned from scratch.

SIPOC

A one-page high-level map of Suppliers, Inputs, Process, Outputs and Customers that fixes the boundaries of an improvement project before detailed mapping begins.

When to use: In the Define phase, immediately after the charter, and any time a team cannot agree where a process starts and stops.

5 Whys

An iterative interrogation technique that moves from a symptom to a systemic root cause by asking why the previous answer occurred, typically five times.

When to use: For focused, single-cause problems in Analyze, in incident reviews, and inside a fishbone branch to drill one cause deeper.

Fishbone (Ishikawa) Diagram

A structured cause-and-effect diagram that organises all potential causes of a defect into standard categories so the team explores the whole problem space before testing hypotheses.

When to use: Early in Analyze, when a problem has many plausible causes and the team needs a complete, categorised view rather than the first idea in the room.

Formulas library

Every formula with variables, interpretation thresholds and a worked example.

Defects per Million Opportunities (DPMO)

DPMO = (Defects / (Units x Opportunities per Unit)) x 1,000,000

D: Number of defects found (defects)
U: Number of units inspected (units)
O: Defect opportunities per unit (opportunities)

DPMO <= 3.4 — 6 sigma
DPMO <= 233 — 5 sigma
DPMO <= 6210 — 4 sigma
DPMO <= 66807 — 3 sigma
DPMO <= 308538 — 2 sigma
DPMO <= 691462 — 1 sigma

Worked example

An invoicing team processes 1,500 invoices with 4 checkable fields each and finds 27 field errors.

DPMO = 27 / (1,500 x 4) x 1,000,000 = 27 / 6,000 x 1,000,000 = 4,500

Just above 4 sigma — solid, but a Green Belt project could realistically reach 5 sigma.

Try: An invoicing team processes 1,500 invoices with 4 checkable fields each and finds 27 field errors.

Defects per Unit (DPU)

DPU = Defects / Units

D: Number of defects (defects)
U: Number of units produced (units)

DPU < 0.01 — Excellent
DPU 0.01 - 0.10 — Acceptable
DPU > 0.10 — Poor

Worked example

A packaging line makes 2,400 cartons in a shift and QA logs 96 defects.

DPU = 96 / 2,400 = 0.04

4 defects per 100 cartons; combined with FTY this drives the rework cost estimate.

Try: A packaging line makes 2,400 cartons in a shift and QA logs 96 defects.

First Time Yield (FTY)

FTY = Units passed without rework / Units entering the step

Pass: Units passing the step first time (units)
In: Units entering the step (units)

FTY >= 0.99 — Excellent
FTY 0.95 - 0.99 — Acceptable
FTY < 0.95 — Poor

Worked example

A loan-application review receives 500 files; 465 pass first review, 35 go back for correction.

FTY = 465 / 500 = 0.93

7% rework at a single step; measure the other steps to get RTY before choosing where to improve.

Try: A loan-application review receives 500 files; 465 pass first review, 35 go back for correction.

Rolled Throughput Yield (RTY)

RTY = FTY1 x FTY2 x ... x FTYn

FTYn: First Time Yield of each process step (ratio)
n: Number of sequential steps (steps)

RTY >= 0.95 — Healthy end-to-end flow
RTY 0.80 - 0.95 — Watch the weakest step
RTY < 0.80 — Hidden factory

Worked example

Loan process with four steps at FTY 0.93, 0.97, 0.99 and 0.95.

RTY = 0.93 x 0.97 x 0.99 x 0.95 = 0.8484

Roughly 15 of every 100 applications are reworked somewhere — the 0.93 step is the priority.

Try: Loan process with four steps at FTY 0.

Process Capability (Cp)

Cp = (USL - LSL) / (6 x sigma)

USL: Upper Specification Limit (unit of measure)
LSL: Lower Specification Limit (unit of measure)
sigma: Process standard deviation (unit of measure)

Cp < 1.00 — Incapable
Cp 1.00 - 1.33 — Marginal
Cp >= 1.33 — Capable
Cp >= 2.00 — Six Sigma capable

Worked example

A machined shaft must be 20.00 ± 0.30 mm; the process standard deviation is 0.10 mm.

Cp = (20.30 - 19.70) / (6 x 0.10) = 0.60 / 0.60 = 1.00

Potentially capable but with zero margin — reduce variation to reach the 1.33 target.

Try: A machined shaft must be 20.

Process Capability Index (Cpk)

Cpk = min[(USL - mean) / (3 x sigma), (mean - LSL) / (3 x sigma)]

USL: Upper Specification Limit (unit of measure)
LSL: Lower Specification Limit (unit of measure)
mean: Process mean (unit of measure)
sigma: Process standard deviation (unit of measure)

Cpk < 1.00 — Not capable
Cpk 1.00 - 1.32 — Marginal
Cpk >= 1.33 — Capable
Cpk >= 1.67 — Highly capable

Worked example

Same shaft (USL 20.30, LSL 19.70, sigma 0.10) but the process is running at a mean of 20.10 mm.

Upper = (20.30 - 20.10) / 0.30 = 0.667; Lower = (20.10 - 19.70) / 0.30 = 1.333; Cpk = min = 0.667

Cp is 1.00 but Cpk is 0.67 — the process is off-centre by 0.10 mm. Re-centring alone triples the margin.

Try: Same shaft (USL 20.

Takt Time

Takt = Available production time / Customer demand

T: Available working time in the period (minutes)
D: Customer demand in the same period (units)

Cycle time < Takt — Capacity available
Cycle time = Takt — Perfectly balanced
Cycle time > Takt — Cannot meet demand

Worked example

A clinic runs an 8-hour day with two 15-minute breaks (450 productive minutes) and must see 60 patients.

Takt = 450 / 60 = 7.5

Any consultation step averaging over 7.5 minutes creates a queue — balance the line to that beat.

Try: A clinic runs an 8-hour day with two 15-minute breaks (450 productive minutes) and must see 60 patients.

Little's Law

Lead Time = Work in Process / Throughput (exit rate)

WIP: Work in process (items in the system) (items)
TH: Throughput / exit rate (items per day)

Lead time within customer promise — Flow is healthy
Lead time near the promise — Fragile
Lead time beyond the promise — Overloaded queue

Worked example

A support desk has 120 open tickets and closes 30 tickets per day.

Lead time = 120 / 30 = 4

To promise a 2-day response, cap open tickets at 60 or raise closure rate to 60 per day.

Try: A support desk has 120 open tickets and closes 30 tickets per day.